A361093
E.g.f. satisfies A(x) = exp( 1/(1 - x * A(x)^2) - 1 ).
Original entry on oeis.org
1, 1, 7, 97, 2049, 58541, 2114143, 92419965, 4746108769, 280105517881, 18683156508471, 1389960074426969, 114119472522112225, 10249863809271551973, 999746622121255094479, 105236583967331849218741, 11891012005206169120252737, 1435560112909007680593616625
Offset: 0
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Table[n! * Sum[(2*n+1)^(k-1) * Binomial[n-1,n-k]/k!, {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Mar 02 2023 *)
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a(n) = n!*sum(k=0, n, (2*n+1)^(k-1)*binomial(n-1, n-k)/k!);
A361095
E.g.f. satisfies A(x) = exp( 1/(1 - x/A(x)) - 1 ).
Original entry on oeis.org
1, 1, 1, -2, -3, 56, -155, -2736, 34489, 72064, -6599799, 53676800, 1155350581, -32238425088, -3604716947, 14790925735936, -235482791871375, -4972572910452736, 254158358486634001, -1028499606209101824, -202204782754527137939, 5371925138905661440000
Offset: 0
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a(n) = if(n==0, 1, n!*sum(k=1, n, (-n+1)^(k-1)*binomial(n-1, n-k)/k!));
A361096
E.g.f. satisfies A(x) = exp( 1/(1 - x/A(x)^2) - 1 ).
Original entry on oeis.org
1, 1, -1, 1, 17, -339, 4999, -63587, 566145, 3549241, -405637489, 15518099961, -446235202799, 9617693853925, -75522664207017, -7341781870733099, 596513949276803969, -30104875035438797583, 1144712508931072057375, -27381639204739332379151
Offset: 0
A361097
E.g.f. satisfies A(x) = exp( 1/(1 - x/A(x)^3) - 1 ).
Original entry on oeis.org
1, 1, -3, 22, -251, 3816, -71207, 1542640, -36997431, 929097856, -22062115979, 334968255744, 13395424571725, -2177817789105152, 201597999475333329, -16622491076645341184, 1332634806870147259537, -107073894723559010304000
Offset: 0
A363479
E.g.f. satisfies A(x) = exp(x * A(x)^3 * (1 + x * A(x)^3)).
Original entry on oeis.org
1, 1, 9, 160, 4381, 162816, 7663669, 437164288, 29317265625, 2260685099008, 197088986941921, 19170218777296896, 2058199476739788661, 241779221463040000000, 30847476924400409437389, 4247859315849037948911616, 627960846411135123552180529
Offset: 0
A365015
E.g.f. satisfies A(x) = exp( x*A(x)^3/(1 - x * A(x)) ).
Original entry on oeis.org
1, 1, 9, 154, 3997, 140216, 6217549, 333774064, 21051514425, 1526073116032, 125040978948241, 11428407889500416, 1152792683163827413, 127215353330004610048, 15246125111980753585365, 1971966282368187450198016, 273796236099258954747416689
Offset: 0
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Array[#!*Sum[ (# + 2 k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 17, 0] (* Michael De Vlieger, Aug 18 2023 *)
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a(n) = n!*sum(k=0, n, (n+2*k+1)^(k-1)*binomial(n-1, n-k)/k!);
A365016
E.g.f. satisfies A(x) = exp( x*A(x)^3/(1 - x * A(x)^2) ).
Original entry on oeis.org
1, 1, 9, 160, 4345, 159796, 7434199, 418864426, 27732988609, 2110729489048, 181587635465671, 17426825999144926, 1845855944285411425, 213900244312057975348, 26919356609721984494311, 3656322063766897691641666, 533110345129065969043548289
Offset: 0
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Array[#!*Sum[ (2 # + k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 17, 0] (* Michael De Vlieger, Aug 18 2023 *)
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a(n) = n!*sum(k=0, n, (2*n+k+1)^(k-1)*binomial(n-1, n-k)/k!);
Showing 1-7 of 7 results.